Generalized Alpha-Close-to-Convex Functions. (1st November 2009) - Noor, K. Inayat
Abstract : We define the classes G β ( α, k, γ ) as follows: f ∈ G β ( α, k, γ ) if and only if, for z ∈ E = { z ∈ ℂ : | z | < 1 }, | arg { ( 1 - α 2 z 2 ) f ′ ( z ) / e − i β ϕ ′ ( z ) } | ≤ γ π / 2, 0 < γ ≤ 1 ; α ∈ [ 0, 1 ] ; β ∈ ( − π / 2, π / 2 ), where ϕ is a function of bounded boundary rotation. Coefficient estimates, an inclusion result, arclength problem, and some other properties of these classes are studied.